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At my university it's common to call acyclic, connected graph a tree. We distinguish between rooted and unrooted trees. For example, minimal spanning tree doesn't really have to be rooted, it just has no cycles.

> acyclic, connected graph a tree

This is the graph theoretic definition of a tree.

Tree is a graph without any cycles, hence the definition still holds. And yes, you can have multiple roots in a tree, ex:

a --> c <---b ^ d-----|

Yes, it's not a tree any more. Which is why I believe this was not the question.